ElementType Picker - save selection issue

I tried to set up the Player template but I can see that picker values are not saved correctly. After opening selection value is unticked.
I guess for time being I will swap to element ID as I can save in the panel and this will guarantee value will be always there

The picker picks that specific element on that specific document. If you change the document, although the element will have the same integer id, it is still not going to be selected.